Adaptive batching for Gaussian process surrogates with application in noisy level set estimation

We develop adaptive replicated designs for Gaussian process metamodels of stochastic experiments. Adaptive batching is a natural extension sequential design heuristics with the benefit replication growing as response features are learned, inputs concentrate, and metamodeling overhead rises. Motivated by problem learning level set mean simulator response, we five novel schemes: Multi-Level Batching (MLB), Ratchet (RB), Batched Stepwise Uncertainty Reduction (ABSUR), Design Allocation (ADSA), Deterministic (DDSA). Our algorithms simultaneously (MLB, RB, ABSUR) or sequentially (ADSA DDSA) determine respective number replicates. Illustrations using synthetic examples an application in quantitative finance (Bermudan option pricing via Regression Monte Carlo) show that brings significant computational speed-ups minimal loss modeling fidelity.